Details
| Original language | English |
|---|---|
| Pages (from-to) | 1061-1064 |
| Number of pages | 4 |
| Journal | Forum mathematicum |
| Volume | 30 |
| Issue number | 4 |
| Publication status | Published - 1 Jul 2018 |
| Externally published | Yes |
Abstract
Answering a question of Pálfy and Pyber, we first prove the following extension of the k(GV)-problem: Let G be a finite group and let A be a coprime automorphism group of G. Then the number of conjugacy classes of the semidirect product G × A is at most |G|.As a consequence,we verify Brauer's k(B)-conjecture for π-blocks of π-separable groups which was proposed by Y. Liu. This generalizes the corresponding result for blocks of p-solvable groups.We also discuss equality in Brauer's Conjecture. On the other hand,we construct a counterexample to a version of Olsson's Conjecture for π-blocks which was also introduced by Liu.
Keywords
- Brauer's k(B)-conjecture, k(GV)-problem, π-blocks
ASJC Scopus subject areas
- Mathematics(all)
- General Mathematics
- Mathematics(all)
- Applied Mathematics
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In: Forum mathematicum, Vol. 30, No. 4, 01.07.2018, p. 1061-1064.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Solution of Brauer's k(B)-conjecture for π-blocks of π-separable groups
AU - Sambale, Benjamin
N1 - Funding information: This work is supported by the German Research Foundation by the projects SA 2864/1-1 and SA 2864/3-1.
PY - 2018/7/1
Y1 - 2018/7/1
N2 - Answering a question of Pálfy and Pyber, we first prove the following extension of the k(GV)-problem: Let G be a finite group and let A be a coprime automorphism group of G. Then the number of conjugacy classes of the semidirect product G × A is at most |G|.As a consequence,we verify Brauer's k(B)-conjecture for π-blocks of π-separable groups which was proposed by Y. Liu. This generalizes the corresponding result for blocks of p-solvable groups.We also discuss equality in Brauer's Conjecture. On the other hand,we construct a counterexample to a version of Olsson's Conjecture for π-blocks which was also introduced by Liu.
AB - Answering a question of Pálfy and Pyber, we first prove the following extension of the k(GV)-problem: Let G be a finite group and let A be a coprime automorphism group of G. Then the number of conjugacy classes of the semidirect product G × A is at most |G|.As a consequence,we verify Brauer's k(B)-conjecture for π-blocks of π-separable groups which was proposed by Y. Liu. This generalizes the corresponding result for blocks of p-solvable groups.We also discuss equality in Brauer's Conjecture. On the other hand,we construct a counterexample to a version of Olsson's Conjecture for π-blocks which was also introduced by Liu.
KW - Brauer's k(B)-conjecture
KW - k(GV)-problem
KW - π-blocks
UR - http://www.scopus.com/inward/record.url?scp=85041061220&partnerID=8YFLogxK
U2 - 10.1515/forum-2017-0147
DO - 10.1515/forum-2017-0147
M3 - Article
AN - SCOPUS:85041061220
VL - 30
SP - 1061
EP - 1064
JO - Forum mathematicum
JF - Forum mathematicum
SN - 0933-7741
IS - 4
ER -